Presentation Transcript

Objectives • Why do networks expand and contract? • Do networks self-organize into hierarchies? • Roads - an emergent property? • Can investment rules predict location of network improvement? • How can this improved knowledge help in planning transportation networks?

How networks change with time? • State of a network node changes • Travel time of a link changes • Capacity of a link changes • Flow on a link changes • New links and nodes are added • Existing links are removed • System properties, like congestion, change over time

How to model a network as a complex system? • Links and nodes are agents • Agent properties • Rules of interaction that determine the state of agents in the next time step • Spatial pattern of interaction between agents • External forces and variables • Initial states

Transportation network as a complex system • Network is split into two layers • Network layer • Land use layer • Network is modeled as a directed graph • Land Use Layer has small land blocks as agents that determine the populations and land use

Network Layer Land Use Layer Figure 1: Splitting the system into network layer and land use layer

Land Use and Demography • Small Land Blocks are agents • Population, business activity, and geographical features are attributes • Uniformly distributed and bell shaped land use are modeled • Land use is assumed to be static • Dynamics of land use will be added later

Travel Demand Model • Trip Generation • Using Land use model trips produced and attracted are calculated for each cell • Cells are assigned to network nodes using voronoi diagram • Trips produced and attracted are calculated for a network node using voronoi diagram

Travel Demand Model(Contd.) • Traffic Assignment • Path with least cost of traveling • Cost of traveling a link is Where, la is length of link a va is speed of link a  is value of time o is tax rate 1, 2 are coefficients

Revenue Model • Toll is the only source of revenue • Annual revenue generated by a link is total toll paid by the travelers Where, coefficients are same as coefficients used in traveling cost function • A central revenue handling agent can be modeled

Cost Model • Assuming only one type of cost • Cost of a link is Where, c is cost rate, 1, 2, 3 are coefficients. • Introducing more cost functions makes the model more complicated and probably more realistic

Network Investment Model • A link based model • Speed of a link improves if revenue is more than cost of maintenance, drops otherwise Where, vat is speed of link a at time step t, • is speed reduction coefficient. • No revenue sharing between links: Revenue from a link is used in its own investment

Conclusions • Succeeded in growing transportation networks • Sufficiency of simple link based revenue and investment rules in mimicking the network structure • Hierarchical structure of transportation networks is a property not entirely a design • Future work will help in better understanding of network dynamics